MSc TPFE/4th Year Mechanical and Aerospace Advanced CFD Laboratory

Laminar Flow in tube bundlesusing Star CCM+

1 IntroductionFlows through tubes bundles are encountered in many heat exchanger applications. Oneexample is in nuclear power plants where the nuclear fuel rods are cooled by passingcold water over them, but similar arrangements are also employed in more conventionalexchangers. The objective of this type of heat exchanger is, of course, to extract as muchheat as possible from the tubes. In a computational study, in order to calculate the heattransfer reliably, it is necessary to resolve the flow around the tubes correctly.

A typical staggered tube bundle configuration, which is to be studied in this exercise,can be seen in Figure 1. It is assumed to consist of a large number of tubes, so the flowaround any one is considered to be identical to that around the others. The computa-tional domain employed is highlighted, which takes advantage of some of the symmetriespresent in the flow. Symmetry conditions are applied on the top and bottom boundaries,whilst periodic conditions (with a prescribed pressure drop) are applied between the eastand west boundaries.

Figure 1: Flow geometry

The flow is to be computed as laminar, and three meshes are provided. The firstone consists of block structured quadrilateral cells with a resolution of 540 cells in total

1

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with 72 points around one cylinder. The second mesh is an unstructured mesh made ofquadrilateral cells (PAVE). The total number of cells is 433 with 64 points around onecylinder. The third mesh (TETRA) is made of triagular elements, with a total number of490 cells with 64 points around one cylinder. The meshes can be seen in Figure 2.

Figure 2: Three types of meshes

The use of a structured mesh means that there are rather highly skewed cells at theinterface between the curved edge of the cylinder and the straight symmetry edge. Theunstructured approach deals with this by removing the constraint of the cell edges havingto lie along the same lines as the block boundaries.

By using these relatively coarse meshes, the influence of the skewness of the grid canbe seen. Although the error introduced can be reduced by refining the mesh, the numberof cells required to reduce the error significantly is different for each meshing technique.This means that before doing a mesh refinement study, it is often worth spending someeffort in achieving a grid structure with the least distortion possible.

A converged solution on a very fine grid is also available, allowing comparisons tobe drawn between these grid-independent results and those obtained on the three coarsergrids described above.

2 ObjectivesOne of the objectives of this exercise is to compare the three different types of mesh-ing techniques described above for a complex curved geometry, and assess their relative

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strengths and weaknesses in terms of solution accuracy.A second objective is to gain more experience in using a wider range of CFD and

other software tools for simulations and post-processing; in particular here using the StarCCM+ program to perform the flow simulations.

3 InvestigationsFirst, follow the instructions given below to run the case using the block-structured grid(BLOCK), and post-process the results. Then, follow the same steps to compute andexamine the solution for the other two grids.

Comparisons should be drawn between the computed solutions on the different grids,and the grid-independent one from the provided fine grid solution. Qualitative compar-isons can be made by examining velocity vector plots, contour plots of velocity or pres-sure, and streamlines. For quantitative output, useful comparisons include

• U -velocity component profiles along the periodic boundary (x = 0) and symmetryline (y = 0).

• The flow recirculation length, deduced from the velocity profile along y = 0.

• The computed mass flow rate, conveniently expressed non-dimensionally as theReynolds number based on tube diameter and bulk velocity (Re = Ubd/ν).

• Compute the pressure drop coefficient Kp as in:

∆P = Kp1

2ρU2

b (1)

The pressure drop ∆P/L = 10−5 has to be prescribed as a forcing term F = ∆P/Lwhere L is the distance between the periodic faces.

OPTIONAL: You could also investigate how the pressure drop coefficientKp changeswith Re number. By systematically increasing the viscosity (multiply by 2, 4, 8 ...) youcan decrease Re while keeping the same ∆P . Calculate the quantity KpRe and see if itremains constant. How does the recirculation region change with Re?

4 Reporting RequirementsStudents should submit a short report within 2 weeks of the laboratory. The report shouldcontain a brief introductory section, outlining the nature of the investigations conducted,and should then describe and discuss (with the aid of a selection of figures) the resultsobtained and comparisons between the various solutions. Excluding tables and figuresthis is unlikely to require more than 4–5 pages of text.

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5 Guide to Running Star CCM+First download the meshs required from the website:http://cfd.mace.manchester.ac.uk/twiki/bin/view/Main/StarCCMTutorialLaminarFlow (thisweb address is case sensitive). Star CCM+ can be found on the computers in the computercluster. It is installed under EPS, MACE as shown in Figure 3.

Figure 3: How to launch Star CCM+ 5.04.006

Once the Star CCM+ window has opened go to file and select new simulation as inFigure 4.

Figure 4: Setting up a simulation in Star CCM+

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A new window labelled Create a New Simulation is going to open, leave thesettings as default and click on OK. After the case has been set up, click on file again andthen select Import as in Figure 5.

Figure 5: Setting up a simulation in Star CCM+

This is going to open another window. Navigate to the mesh Bundle_block.ccmand open it. This is going to give an import mesh option menu, keep the default settingsand select ok. If every thing has been done correctly then a fluid region should show upas shown in Figure 6.

Figure 6: Setting up a simulation in Star CCM+

Now this fluid domain has to be split into different regions, so that boundary condi-

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tions can be assigned. Expand the Regions tab as shown in Figure 7

Figure 7: Setting up a simulation in Star CCM+

Select Split by Angle . Another window with several options on splitting theboundaries by angle is going to appear as in Figure 8. Add the boundary to the Selectedlist and leave the setting as default and click on Apply. Note that new boundaries aregoing to be added under the Boundaries tab

Figure 8: Setting up a simulation in Star CCM+

Now the Default_Boundary_Region2 and Default_Boundary_Region3have to be further divided and can be done by splitting the domain by angle in the sameway as done previously. The only difference is that this time the prescribed angle is goingto be 30 as in Figure 9

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Figure 9: Setting up a simulation in Star CCM+

The boundary conditions are to be defined now and can be done by selecting theregions under the Boundaries tab. The Default_Boundary_Region should beassigned a Symmetry Plane as in Figure 10

Figure 10: Setting up a simulation in Star CCM+

Similarly the respective boundary conditions for other boundaries can be setup and

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are shown in Table 1

Default_Boundary_Region Symmetry PlaneDefault_Boundary_Region2 WallDefault_Boundary_Region22 Symmetry PlaneDefault_Boundary_Region23 Symmetry PlaneDefault_Boundary_Region3 WallDefault_Boundary_Region32 WallDefault_Boundary_Region33 WallDefault_Boundary_Region34 WallDefault_Boundary_Region35 Symmetry PlaneDefault_Boundary_Region4 Symmetry Plane

Table 1: Boundary conditions

Now the physical conditions for the simulation can be set-up by expanding the Continuatab. Double click on the Models tab as in Figure 11

Figure 11: Setting up a simulation in Star CCM+

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A new window for physics model selection would appear. This allows the user toselect the required solution methods and models to be used for the calculation as in Fig-ure 12

Figure 12: Setting up a simulation in Star CCM+

In the Physics Model Selection select Steady under Time calculation,Gas under the Material, Segregated Flow under Flow , Constant Densityunder Equation of State and Laminar under the Viscous Regime. The se-lection is shown in Figure 13. Once every thing has been selected click on Close.

Figure 13: Setting up a simulation in Star CCM+

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Once the Physics Model Selection is complete the material properties i.e.density and dynamic viscosity have to be changed. Expand the Models tab and thenexpand the Gas tab as in Figure 14. Change the Density to ρ = 1.17862kg/m3 and thedynamic viscosity to µ = 1.83× 10−5Ns/m2.

Figure 14: Setting up a simulation in Star CCM+

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After updating the material properties the periodic boundary conditions are to bedefined. This can be done by selecting the Default_Boundary_Region 32 andDefault_Boundary_Region 33 at the same time and then right clickingDefault_Boundary_Region 32, a drop down menu would appear go to create in-terface and select periodic as in Figure 15. If this is done correctly then a new tab calledInterfaces would appear in the simulation menu.

Figure 15: Setting up a simulation in Star CCM+

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Now expand the Interface tab and select the tab labelled Periodic a tablewould appear in the properties menu as in Figure 16. Change the Interface type toFully-Developed Interface as shown in Figure 16.

Figure 16: Setting up a simulation in Star CCM+

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Expand Physics Values tab under the Periodic1 tab and specify the pressurejump as −1× 10−5Pa as shown in Figure 17.

Figure 17: Setting up a simulation in Star CCM+

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After setting up the Periodic boundary conditions expand the Stopping Criteriatab and set the Maximum Steps to 2000 as shown in Figure 18. This is the maximumnumber of iterations to be used by the simulation.

Figure 18: Setting up a simulation in Star CCM+

In order to run the simulation initilise the solution by clicking on and then click

on to run the simulation for the prescribed number of iterations. After the simulationhas been started a graph appears on the screen which shows the residuals for the respec-tive simulation. Once the calculation has finished the following message appears in theOutput window.

Stopping criterion Maximum Steps satisfied.

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6 Post-Processing in Star CCM+In order to analyse the results from the simulation the integrated post-processing toolsavailable in StarCCM+ are used. In order to make plots from the simulation, nevigateto the Scenes tab and right click on it, a drop down menu would appear. Then go toNew Scene and select Scalar as in Figure 19. If this step is followed correctly a newtab Scalar Scene 1 should appear under the Scenes tab.

Figure 19: Post-Processing in Star CCM+

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Now expand Scalar Scene 1 → Displayers → Scalar 1 and right clickon the Parts tab under the Scalar 1 tab then select Edit as in Figure 20.

Figure 20: Post-Processing in Star CCM+

A new window is going to open which gives the option to select the regions to bedisplayed in the plot. Check the box next to Regions as in Figure 21 and click OK

Figure 21: Post-Processing in Star CCM+

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After selecting the parts select the Scalar Field tab and then select the Functionin the Scalar Field properties window as in Figure 22. Note that in Figure 22 thei,j and k represent the respective X,Y and Z components of velocity. Select the icomponent of the velocity.

Figure 22: Post-Processing in Star CCM+

If every thing has been done correctly a plot shown in Figure 23 should show up inthe visualisation window.

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Figure 23: Post-Processing in Star CCM+

In order to make the plots smooth select Scalar 1 tab under the Scalar Scene 1tab, then in the properties window change the Contour Style to Smooth Filledas in Figure 24

Figure 24: Post-Processing in Star CCM+

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The default pressure option in Star CCM+ is given as absolute pressure rather thanthe relative presure. In this study relative pressure is required so in order to rectifythis a field function is used to post-process the pressure field in the simulation. A newfield function can be introduced by expanding the Tools tab and then right clicking theField Functions tab and selecting New as in Figure 25

Figure 25: Post-Processing in Star CCM+

A new field function labelled as User Field Function1 is going to appear un-der the Field Functions tab. Select the User Field Function1 and changethe Definition in the properties window to :

$Pressure+(((1e-5)*($${Position}[0]))/2)

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The definition for the field function is shown in Figure 26. Now in order to plotpressure follow the same procedure as done for velocity and make a new scalar scene, butthis time select the User Field Function1 instead of velocity when specifying thescalar.

Figure 26: Post-Processing in Star CCM+

A quantitative way of comparing the results is to plot velocity profiles along particularlines. For this exercise the bottom symmetry line at y = 0 and the periodic line at x = 0can be used. Before creating the line make sure that a Scalar Scene is open in thevisualisation window. Then right click on the Derived Parts tab go to New Partsthen probe and then select Line as in Figure 27. An input menu is going to appearin the tabs menu as in Figure 28 and the line is going to be visible in the visualisationwindow. To create the line at the symmetry plane y = 0 enter the points as (0.5, 0, 0.2)and (1.5, 0, 0.2) and set the resolution to 20 points. Click on Create and then on Close

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Figure 27: Post-Processing in Star CCM+

Figure 28: Post-Processing in Star CCM+

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To create another probe line along the periodic plane x = 0 follow the same procedureas done for the y = 0 plane, but now use the points as (0, 0.5, 0.2) and (0, 1, 0.2) and setthe resolution to 10 points.To plot the velocity or pressure profiles along the lines created earlier right click on thePlots tab go to New Plot and then select XY Plot as in Figure 29

Figure 29: Post-Processing in Star CCM+

A new tab labelled XY Plot1 is going to appear under the Plots tab. Select theXY Plot1 tab and select the Parts in the properties window then select line-probeas in Figure 30

Figure 30: Post-Processing in Star CCM+

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Now expand the Y Types tab under XY Plot1 tab and select the Scalar in theproperties window as in Figure 31. Select i component of the velocity.

Figure 31: Post-Processing in Star CCM+

In order to reset the scale in the XY plot the expand the XY Plot1→ YType 1 andselect line-probe. Then in the properties window change the X Offset to −0.5 asin Figure 32

If every thing has been done correctly then an XY plot should be obtained in thevisualisation window as in Figure 33

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Figure 32: Post-Processing in Star CCM+

Figure 33: Post-Processing in Star CCM+

Now repeat these steps to obtain a new XY plot along the x = 0 plane. The differencein this plot is that the position has a different direction to the position in the previous plotand the value of the X Off set is 1.0. To change the position for this plot expand therespective XY Plot tab and then expand the X Type tab. In the properties window

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change the direction to [0.0,-1.0,0.0] as in Figure 34

Figure 34: Post-Processing in Star CCM+

Note that all the figures can be exported by right clicking on the respective sceneand selecting export. In case of XY plots a spread sheet is exported and can be used byMicrosoft Excel or MATLAB.

7 Fine Grid SolutionsAfter post processing the results for the Block mesh, the same procedure can be appliedto the other two meshes, i.e. PAVE and TETRA. Create a new case for all the mesh andfollow the same instructions.After the results for the three meshes have been obtained, they can be compared with thereference data available on the website. These results were obtained with a mesh of 30180cells using the same version of Star CCM+, and can be used to compare the coarse meshresults obtained during the exercise.